Simulating a Weighted Die?
Yes

By adding an extra rigid body constrained inside the die as a weight, you can do this:


Add a small object to act as the weight (e.g. an icosphere) and position it inside the die on the opposite side of the 6. Make it a dynamic rigid body and adjust the mass as needed:


Add a Fixed rigid body constraint connecting the weight to the die.


Select the weight and then the die (so that the die is active).
Press Connect in 3D view > Tool Shelf (T) > Rigid Body Tools.
Ensure that the Type is set to Fixed:



With the newly created constraint empty selected, make sure collisions between the weight and the die are disabled:


Make a simulation and be amazed as you roll 6 every time ;)



I know.. I misread your question and thought you wanted lucky dice, but obviously this technique works for simulating unlucky dice too.